I don't think freedom of choice is possible in an absolute sense because that would imply the ability to make decisions without influence or dependency from other processes, which seems impossible to me since we are physical beings subject to the laws of the universe for example.
Free choice in an absolute sense is like an effect happening without cause in my opinion.
A lot of the actions we commit to everyday are not always by choice either, although we think they are, but if you really think about it, they are not. Like going to the bathroom for example. You might make such a choice, or you might just go do it, it depends on the situation, but most people would argue that every time you go to the bathroom you are making a choice to do so. I don't see how that is possible.
That idea applies to a lot things, even sexual activity. Do you really choose to have sex every time you do it? I think the honest answer is no because sometimes we just DO things without actually making a decision to do them or not.
Some people seem to really have a problem with that. I think it's because we would like to think of ourselves as not being a 'slave' to something and in control of everything. It also brings into question responsibility and accountability. If people don't actually make a conscious decision for everything they do then how can they be held accountable for it, like morally for example, or legally?
I don't think free choice is actually supported in a biblical sense either though, at least in a Christian context. I think the modern christian idea of it is one that is manufactured in order to place moral responsibility on people that otherwise would not be possible without the idea of free choice. It also doesn't seem fair or just for God to send people to hell that weren't given a choice in the matter, does it?